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Author: Catherine Louise Olsen Publisher: American Mathematical Soc. ISBN: 9780821860380 Category : Mathematics Languages : en Pages : 80
Book Description
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.
Author: Catherine Louise Olsen Publisher: American Mathematical Soc. ISBN: 9780821860380 Category : Mathematics Languages : en Pages : 80
Book Description
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.
Author: Catherine Louise Olsen Publisher: American Mathematical Soc. ISBN: 0821822950 Category : Analytic functions Languages : en Pages : 78
Book Description
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm and semi-Fredholm theory.
Author: Jeffrey Stephen Fox Publisher: American Mathematical Soc. ISBN: 0821851527 Category : Mathematics Languages : en Pages : 202
Book Description
This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on $K$-Homology and Index Theory, held in August, 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple $p$-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.
Author: Rufus Willett Publisher: Cambridge University Press ISBN: 1108853110 Category : Mathematics Languages : en Pages : 595
Book Description
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Author: J. Dixmier Publisher: Elsevier ISBN: 0080960154 Category : Mathematics Languages : en Pages : 479
Book Description
In this book, we study, under the name of von Neumann algebras, those algebras generally known as “rings of operators“ or “W*-algebras.“ The new terminology, suggested by J. Dieudonng, is fully justified from the historical point of view. Certain of the results are valid for more general algebras. We have, however systematically avoided this kind of generalization, except when it would facilitate the study of von Neumann algebras themselves. Parts I and I1 comprise those results which at present appear to’be the most useful for applications, although we do not embark on the study of those applications. Part 111, which is more technical, is primarily intended for specialists; it is virtually independent of Part 11.
Author: Gerald J. Murphy Publisher: Academic Press ISBN: 0080924964 Category : Mathematics Languages : en Pages : 297
Book Description
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Author: Catherine Louise Olsen
Author: Catherine Louise Olsen
Author: Catherine Louise Olsen
Author: Catherine Louise Olsen
Author: Hideki Kosaki
Author: Serban Stratila
Author: Jeffrey Stephen Fox
Author: Allan Sinclair
Author: Rufus Willett
Author: J. Dixmier
Author: Gerald J. Murphy